
<center>
<b><font size="+2">Entering Formulas</font></b>
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<ul type="square">

<li><a href="http://webwork.maa.org/wiki/Available_Functions" target="_new">Link to a list of all available functions</a><br /><br /></li>

<li><u>Formulas must use the correct variable(s):</u>
<blockquote>
For example, a function of time &nbsp; <tt>t</tt> &nbsp; could be &nbsp; <tt>-16t^2 + 12</tt>, while &nbsp; <tt>-16x^2 + 12</tt> &nbsp; would be incorrect. 
</blockquote>
</li>

<li><u>Examples of valid formulas:</u>
<blockquote>
<tt>5*sin((pi*x)/2)</tt> &nbsp;&nbsp;or&nbsp;&nbsp; <tt>5 sin(pi x/2)</tt><br />
<tt>e^(-x)</tt> &nbsp;&nbsp;or&nbsp;&nbsp; <tt>e**(-x)</tt> &nbsp;&nbsp;or&nbsp;&nbsp; <tt>1/(e^x)</tt><br />
<tt>abs(5y)</tt> &nbsp;&nbsp;or&nbsp;&nbsp; <tt>|5y|</tt><br />
<tt>sqrt(9 - z^2)</tt> &nbsp;&nbsp;or&nbsp;&nbsp; <tt>(9 - z^2)^(1/2)</tt><br />
<tt>24</tt> &nbsp;&nbsp;or&nbsp;&nbsp; <tt>4!</tt> &nbsp;&nbsp;or&nbsp;&nbsp; <tt>4 * 3 * 2 * 1</tt><br />
<tt>pi</tt> &nbsp;&nbsp;or&nbsp;&nbsp; <tt>4 arctan(1)</tt> &nbsp;&nbsp;or&nbsp;&nbsp; <tt>4 atan(1)</tt> &nbsp;&nbsp;or&nbsp;&nbsp; <tt>4 tan^(-1)(1)</tt><br />
</blockquote>
</li>

<li><u>Entering logarithms:</u>
<blockquote>In this question, use <code>ln(x)</code> for natural log, 
and <code>log(x)</code>, <code>logten(x)</code> or <code>log10(x)</code> for 
the base 10 logarithm.  Enter log base b as <code>ln(x)/ln(b)</code>.
</blockquote>
</li>

<li><u>Examples of constants used in formulas:</u>
<blockquote><tt>pi</tt>, <tt>e = e^1</tt></blockquote>
</li>

<li><u>Examples of operations used in formulas:</u>
<blockquote>Addition <tt>+</tt>, subtraction <tt>-</tt>, multiplication <tt>*</tt>, division <tt>/</tt>, exponentiation <tt>^</tt> (or <tt>**</tt>), factorial <tt>!</tt>
</blockquote>
</li>

<li><u>Examples of functions used in formulas:</u>
<blockquote>
<tt>sqrt(x) = x^(1/2)</tt>, <tt>abs(x) = | x |</tt><br />
<tt>2^x, e^x, ln(x), log10(x)</tt> <br />
<tt>sin(x), cos(x), tan(x), csc(x), sec(x), cot(x)</tt><br />
<tt>arcsin(x) = asin(x) = sin^(-1)(x)</tt><br /> 
<tt>arccos(x) = acos(x) = cos^(-1)(x)</tt><br />
<tt>arctan(x) = atan(x) = tan^(-1)(x)</tt><br />
</blockquote>

<li><u>Sometimes formulas must be simplified:</u>
<blockquote>
For example, &nbsp; <tt>6x + 5 - 2x</tt> &nbsp; should be simplified to &nbsp; <tt>4x + 5</tt>
</blockquote>
</li>

<li><u>Sometimes, certain operations are not allowed.</u>
<blockquote>Usually, the operations that are not allowed include addition <tt>+</tt>, subtraction <tt>-</tt>, multiplication <tt>*</tt>, division <tt>/</tt>, and exponentiation <tt>^</tt> (or <tt>**</tt>).  When these operations are not allowed, it is usually because you are expected to be able to simplify your answer, often without using a calculator.</blockquote>
</li>

<li><u>Sometimes, certain functions are not allowed.</u>  
<blockquote>Usually, the functions that are not allowed include square root <tt>sqrt( )</tt>, absolute value <tt>| |</tt> (or <tt>abs( )</tt>), as well as other named functions such as <tt>sin( )</tt>, <tt>ln( )</tt>, etc.  When these functions are not allowed, it is usually because you are expected to be able to simplify your answer, often without using a calculator.</blockquote>
</li>

</ul>
